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%I #25 Jul 03 2023 00:53:14
%S 1,1,1,1,0,1,1,1,2,0,1,1,0,1,0,1,2,2,1,0,0,1,1,1,1,0,2,1,0,0,1,1,2,2,
%T 0,2,0,1,0,0,2,0,1,1,0,1,1,1,2,1,2,0,0,2,0,1,2,0,1,0,0,1,1,1,0,2,1,2,
%U 0,0,1,2,2,0,1,1,0,0,1,0,3,2,1,0,0,1,0,1,2,0,0,1,0,1,0,1,2,2,3,1,0,2,1,0,0
%N Expansion of Sum_{k>0} x^k / (1 + x^(4*k)).
%F G.f.: Sum_{k>0} (-1)^(k-1) * x^(4*k-3) / (1 - x^(4*k-3)).
%F a(n) = Sum_{d|n, d==1 (mod 4)} (-1)^((d-1)/4).
%t a[n_] := DivisorSum[n, (-1)^((# - 1)/4) &, Mod[#, 4] == 1 &]; Array[a, 100] (* _Amiram Eldar_, Jul 03 2023 *)
%o (PARI) a(n) = sumdiv(n, d, (d%4==1)*(-1)^((d-1)/4));
%Y Cf. A002654, A364011.
%Y Cf. A364031, A364032.
%K nonn
%O 1,9
%A _Seiichi Manyama_, Jul 01 2023
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